How to create a fire/light effect in a spaceship engine
When dealing with these effects, generally you have 2 ways - create some geometry with high amount of lighting and use volumetrics for them or fake these effects with compositor. 

Using volumetric materials

You should have some geometry providing actual rays of light; this may be some basic mesh which has forms of rays, or particles emitted from somewhere, forming cloud of light. Then with using volume materials you'll get desired effect.

To begin, either model basic form of rays as mesh as @PGmath suggested or create particles system on the object, which is supposed to emit light, and render those particles as volumetric halos with using Point Density texture which is what I did. See What is Point Density for more info about this feature. See Halo particles don't render in Cycles for details about texture setup (Note: accessible starting from Blender 2.76).


Add a particle system to the object, with vertex groups point it to be emitted from adjacent place (via Vertex Group rollout in particle system's settings). Set up a force field / emission direction for particles to form basic shape of the rays. You might want to disable gravity for particles to stop them falling down while being emitted.
Create several cubes which will contain particles inside. They will serve as domains for volumetric materials. I added particles coming from the floor too, for adding a bit of volumetric lighting across the scene. 



Also you may want to position illuminating objects on different layers; this could improve scene allowing to:


overlay objects that illuminate scene while post-processing; this can save render times quite a bit.
control reflections / refractions if needed. See Post-processing Lightsabers in Blender for more info.

In material setup for the domains add Texture > Point Density and Shader > Emission shader which will be connected to Volume output socket of Material Output node. Set Point Density to Particle System mode and choose adjacent one. You may want to add Math node in order to control amount of final effect.


Play animation to let particles emit. After rendering and a bit of post-processing you'll get something like glow where particles are located.




Faking effect in compositor

While you will get nice result with volumetric material it's very heavy for rendering. And since you asked about animation the rendering times may be even more important. Hence it may be worth trying to fake it with post-processing (at least, part of effect). From this point of view, I think How to render lightning in Cycles is related with only exception for actual object.
In case of this scene, I used following steps:


Model the objects, apply emissive material for adjacent parts. Render the image.
In Composite nodes with keying get part of image which is going to be heavily processed. Create a mask which will control where post-processing will occur. Overlay them together.




The Post-processing group is the one used in the first way and it was used for refining the result (adding Glare, Sunbeams, vignette, desaturation of some parts of image and Lens Distortion).  

Final result:



The rendering is ~ 15 times less.

There's a lot of room for improving:


if considering caustics in render it may be a bit more complicated to setup;
the result with volumetric materials lacks gradient fade out and consistence of light; result with compositing has too short rays etc.


It may depend on the actual scene requirements / limitations.